Bicovariance and Bispectrum of ENSO index and its impact in nonlinear predictability
<p>El Ni&#241;o Southern Oscillation (ENSO) index has been shown as a non-Gaussian and nonlinear stochastic process. Here we assess the statistical significance of non-Gaussianity and non-linearity through the analysis of third-order statistics of El Ni&#241;o 3.4 index in the period 1870&#8211;2018, namely the bicovariance (lagged third-order moments) and bispectrum (its 2D Fourier transform). The analysis of bicovariance reveals a tendency for extreme (weak) ENSO signal in the Boreal Spring to be followed by la Ni&#241;as (El Ni&#241;os) in the forthcoming Boreal Winter, thus contributing for a nonlinear attenuation of the ENSO Spring Predictability Barrier. The bispectrum provides a spectral decomposition of skewness in a similar way of the spectral decomposition of variance. &#160;Positive and negative real bispectrum values identify triadic phase synchronizations (at frequencies f1, f2 and f1+f2, mostly in the period range 2&#8211;6 years) contributing respectively to extreme El Ni&#241;os and La Ni&#241;as. The known positive ENSO skewness and the main features of the ENSO bicovariance and bispectrum are shown to be well reproduced by fitting a bilinear stochastic model where the influence of non-observed variables is simulated by a delayed multiplicative noise, being able to generate non-Gaussianity and non-linearity. The model shows improved forecasts, with respect to benchmark linear models, up to four trimesters ahead, especially of the amplitude of extreme El Ni&#241;os. The authors would like to acknowledge MISU (Meteorological Institute at Stockholm University) and the financial support FCT through project&#160; &#160;UIDB/50019/2020 &#8211; IDL and project JPIOCEANS/0001/2019 (ROADMAP: &#8217;The Role of ocean dynamics and Ocean&#8211;Atmosphere interactions in Driving cliMAte variations and future Projections of impact&#8211;relevant extreme events&#8217;).</p>